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Stability and Hopf bifurcation dynamics of a food chain system: plant–pest–natural enemy with dual gestation delay as a biological control strategy

Stability and Hopf bifurcation dynamics of a food chain system: plant–pest–natural enemy with... In this paper, a food chain system with gestation delay for both pest and the natural enemy is proposed. Here the boundedness of the system is studied. Stability analysis for all possible equilibrium points is carried out. The thresholds for Hopf bifurcation at interior and the natural enemy free equilibrium states are studied and analyzed. It is observed that the natural enemy free steady state is stable if the gestation delay for the pest is sufficiently low otherwise system observed oscillating behavior. Similar observations established for the interior equilibrium. The sensitivity analysis is performed to find the respective sensitive indices of the variables of the proposed system. Further, simulations have been carried out to support our analytic results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Modeling Earth Systems and Environment Springer Journals

Stability and Hopf bifurcation dynamics of a food chain system: plant–pest–natural enemy with dual gestation delay as a biological control strategy

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References (31)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Earth Sciences; Earth System Sciences; Math. Appl. in Environmental Science; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Mathematical Applications in the Physical Sciences; Ecosystems; Environment, general
ISSN
2363-6203
eISSN
2363-6211
DOI
10.1007/s40808-018-0417-1
Publisher site
See Article on Publisher Site

Abstract

In this paper, a food chain system with gestation delay for both pest and the natural enemy is proposed. Here the boundedness of the system is studied. Stability analysis for all possible equilibrium points is carried out. The thresholds for Hopf bifurcation at interior and the natural enemy free equilibrium states are studied and analyzed. It is observed that the natural enemy free steady state is stable if the gestation delay for the pest is sufficiently low otherwise system observed oscillating behavior. Similar observations established for the interior equilibrium. The sensitivity analysis is performed to find the respective sensitive indices of the variables of the proposed system. Further, simulations have been carried out to support our analytic results.

Journal

Modeling Earth Systems and EnvironmentSpringer Journals

Published: Jan 13, 2018

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